Assessing the value of information to design site investigation and construction quality assurance programs - Risk and Reliability in Geotechnical Engineering - page 483

Te st result Probability

S = successful

0.8

W B = B works

Q = questionable

0.15

U = unsuccessful

0.05

S = successful

0.1

Q = questionable

0.2

F B = B fails

U = unsuccessful

0.7

Figure 13.4 Event tree showing conditional probabilities of possible test outcomes for contaminated lagoon.

(e.g., concentrations of contaminants decrease but at a slow rate relative to the duration
of the pilot test), and an unsuccessful result ( U ). An event tree showing how the prob-
abilities for these test outcomes are related to whether or not the in situ bioremediation
will work at the full scale is shown in Figure 13.4 . An important feature of these condi-
tional probabilities is that they are assessed for a defined set of physical conditions, for
example, P ( S | W B ) is the probability of a successful test result if the geologic, chemical,
and biological conditions at the site are such that the full-scale bioremediation will work.
These conditional probabilities can be assessed by analyzing data from other sites where
both pilot-scale and full-scale implementations were used or more plausibly, since this
technology is new, by simulating pilot-scale and full-scale results over a range of possible
site conditions.
The updated probabilities in the decision tree with additional information are obtained
using Bayes' Theorem

P ( E = ε c Pc ) ()

()

C

Pc () ε =

(13.5)

∑

C ε

P ( E = ε c Pc )

C

allc

For example, the probability that the bioremediation alternative will work given a suc-
cessful pilot test is obtained as

PC ( =− $ 15 MM +∆ cS PW S ) = ( )

B test B

CS

B

PWPW
PWPW

( S ) ()

×
×+×

08 . 05 .

B B

= =

(13.6)

08 . 05 . 01 . 05 .

( S ) () ( + PF S )( ) PF

B B B B

0 400
0 400

. 0 400

0450

.
.

= = = . 0 889

. + 0 050 .

The resulting decision trees for the three possible test outcomes are shown in Figure 13.5 ;
this step is referred to a Posterior decision since it is made after additional information is
obtained. The pilot test will change the preferred alternative to the in situ bioremediation
approach if a successful result is obtained from the pilot test, while it will not change the
preferred alternative if the other possible test outcomes occur.